截尾寿命试验中参数最大似然估计的重对数律

本文对于包含定数和定时截尾寿命试验的混合型寿命试验，研究了分布参数的最大似然估计．基于截尾数据，证明了最大似然估计的收敛速度符合重对数律．     

左截断右删失下一类泛函估计的渐近性质

在左截断右删失下,本文讨论了一类广义Von－Mises泛函估计的渐近性质．在一定条件下,得到了此类泛函估计的强逼近和U-统计量表示,并由此得出它的强相合性、渐近正态性及重对数律．     

KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA

Based on left truncated and right censored dependent data, the estimators of higher derivatives of density function and hazard rate function are given by kernel smoothing method. When observed data exhibit α-mixing dependence, local properties including strong consistency and law of iterated logarithm are presented. Moreover, when the mode estimator is defined as the random variable that maximizes the kernel density estimator, the asymptotic normality of the mode estimator is established.     

B值独立随机元重对数律收敛速度的一般形式

本文讨论了Ｂ值独立同分布（ｉｉｄ）随机元重对数律收敛速度的一般形式,使得Ｄａｖｉｓ＾「１」及Ｇｕｔ＾「２,３」中的一些结果成为特款,同时减弱了Ｄａｖｉｓ结果中的矩条件,并且得到了Ｂ值ｉｉｄ随机元满足有界重对数律的一个充分性条件。作为应用,我们给出了随机足标和的相应结果。     

A law of the iterated logarithm for the product limit estimator with doubly censored data

We establish the law of the iterated logarithm for the product limit estimator, when the data are subject to double censoring. This investigation extends the results available for the model for singly censored data.     

线性模型的最小二乘估计的中偏差及其重对数律

本文研究了线性模型的最小二乘估计的中偏差.通过估计Laplace渐近积分,得到了随机误差为取值于Rd的相互独立同分布随机变量情形下的中偏差与重对数律的结果.     

左截断右删失数据下半参数模型风险率函数估计

文章给出了右删失左截断数据半参数模型下的风险率函数估计,讨论了风险率函数估计的渐近性质,获得了这些估计的渐近正态性,对数律和重对数律.由于假定删失机制服从半参数模型下,从而知道模型的更多信息,因此对于给出参数的极大似然估计,可以改进风险率函数估计的渐近性质.也就是说,删失数据模型具有半参数的辅助信息下, 风险率函数估计的渐近方差比通常的完全非参数的估计的渐近方差更小.这说明加入了额外的信息提高了风险率函数估计的效率.     

NA随机变量列的有界重对数律

通过建立NA随机变量最大部分和的一些概率指数不等式，给出了具有不同分布的NA随机变量列有界重对数律的一些结果，因此推广了由R．Wittmann建立的独立随机变量的相关结果。     

一维Wiener sausage长度的中偏差和重对数律

本文研究一维Wiener sausage.利用布朗运动的相关性质和收缩原理,得到p个Wiener sausage相交部分长度的中偏差和重对数律.     

广义矩估计的重对数律

本文研究了广义矩估计的性质.利用强相合性的条件,得到了广义矩估计满足重对数律的结果.     

THE LAW OF ITERATED LOGARITHM FOR R／S STATISTICS

A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.     

随机左截断数据下乘积限估计的强逼近及其应用

本文建立了左截断数据下乘积限估计的强表示结果,其误差项的收敛速度达到重对数律。作为应用,推出了乘积限估计的重对数律和强逼近等深刻结果。     

分组数据情形下对数正态分布参数的最大似然估计

我们研究了分组数据情形下对数正态分布所含参数的最大似然估计存在且唯一的充要条件，进而得到了最大似然估计具有强相合性及收敛速度服从重对数律的结论。     

Asymptotics for a censored generalized linear model with unknown link function

For censored response variable against projected co-variable, a generalized linear model with an unknown link function can cover almost all existing models under censorship. Its special cases include the accelerated failure time model with censored data. Such a model in the uncensored case is called the single-index model in econometrics. In this paper, we systematically study the asymptotic properties. We derive the central limit theorem and the law of the iterated logarithm for an estimator of the direction parameter. We also obtain the optimal convergence rate of an estimator of the unknown link function in the model.      

RATES OF A.S.CONVERGENCE OF THE ESTIMATION OF ERROR VARIANCE IN LINEAR MODELS

Under appropriate conditions we obtain the best rates of a.s.convergence of estimates5_n~2 of error variance σ~2 and establish the law of iterated logarithm     

A LAW OF ITERATED LOGARITHM FOR THE MLE IN A RANDOM CENSORING MODEL WITH INCOMPLETE INFORMATION

In this article, a law of iterated logarithm for the maximum likelihood estimator in a random censoring model with incomplete information under certain regular conditions is obtained.     

非参数回归函数的随机窗宽核估计的重对数律

设(X,Y),(X_1,Y_1),(X_2,Y_2),…为 i.i.d.二维随机变量序列,具有联合分布F(x,y)及密度 f(x,y).X 的边际分布和密度分别记为 F_X(x)和 f_X(x).记 m(x)=E{Y|X=x)}为 Y 对 X 的回归函数.为估计 m(x),Nadaraya 和 watson 独立地引进了如下形式的核估计     

扩散过程在Holder范数下的局部 Strassen重对数律

在该文中,作者应用扩散过程在Holder范数下的大偏差得到了扩散过程在Holder范数下的局部Strassen重对数律. 并且还得到了重Ito积分的泛函重对数律.     

A note on some laws of the iterated logarithm

Some function space laws of the iterated logarithm for Brownian motion with values in finite and infinite dimensional vector spaces are shown to follow from Hincin's classical law of the iterated logarithm and some martingale techniques. A law of the iterated logarithm for Brownian motion in a differentible manifold is also stated.     

扩散过程在Hlder范数下的局部Strassen重对数律

在该文中,作者应用扩散过程在Holder范数下的大偏差得到了扩散过程在Holder范数下的局部Strassen重对数律．并且还得到了重It■积分的泛函重对数律．